**Syllabus**

**The Basics**

- The order of operations
- Evaluating expressions
- Simplifying algebraic expressions

**Matrices**

- Basic matrix operations
- Matrix multiplication
- Determinants
- Matrix inverses
- Cramer’s Rule
- Matrix equations
- Geometric transformations with matrices

**Complex Numbers**

- Adding / subtracting / multiplying / absolute value of complex numbers
- Graphing complex numbers
- Rationalizing imaginary denominators

**Radical Functions and Rational Exponents**

- Simplifying radical expressions
- Operations with radical expressions
- Dividing radical expressions
- Relating rational exponents and radical expressions
- Evaluating rational exponent expressions
- The laws of exponents
- Solving radical equations
- Solving rational exponent equations
- Graphing radical functions
- Domain and range of radical functions

**Rational Expressions**

- Graphing simple rational expressions
- Graphing general rational expressions
- Simplifying rational expressions
- Multiplying / dividing rational expressions
- Adding / subtracting rational expressions
- Complex fractions
- Solving rational equations

**Sequences and Series**

- General sequences
- Arithmetic sequences
- Geometric sequences
- Arithmetic and geometric mean
- General series
- Arithmetic series
- Geometric series
- Infinite geometric series

**Equations and Inequalities**

- Solving multi-step equations
- Work word problems
- Distance-rate-time word problems
- Mixture word problems
- Solving absolute value equations
- Solving multi-step inequalities
- Solving compound inequalities
- Solving absolute value inequalities

**Quadratic Functions and Inequalities**

- Graphing quadratic functions
- Solving quadratic equations by graphing
- Factoring quadratic trinomials
- Factoring special case trinomials
- Solving quadratic equations by taking square roots
- Solving quadratic equations by factoring
- Completing the square
- Solving quadratic equations by completing the square
- Solving quadratic equations using the Quadratic Formula
- The discriminant
- Graphing quadratic inequalities

**General Functions**

- Evaluating functions
- Function operations
- Inverse functions

**Conic Sections**

- Properties of parabolas
- Writing equations of parabolas
- Properties of circles
- Writing equations of circles
- Properties of ellipses
- Writing equations of ellipses
- Properties of hyperbolas
- Writing equations of hyperbolas
- General conic sections
- Systems of quadratic relations

**Exponential and Logarithmic Functions**

- Graphing exponential functions
- Solving exponential equations not requiring logarithms
- Rewriting logarithms
- Evaluating logarithms
- Logarithms and exponential functions as inverses
- Properties of logarithms
- Common logarithms
- Natural logarithms
- Solving exponential equations requiring logarithms
- Solving logarithmic equations
- Graphing logarithmic functions

**Linear Relations and Functions**

- Graphing linear equations
- Writing linear equations
- Graphing absolute value equations
- Graphing linear inequalities
- Systems of Equations and Inequalities
- Graphing systems of two linear inequalities
- Solving systems of two linear equations by graphing
- Solving systems of two linear equations by elimination
- Solving systems of two linear equations by substitution
- Systems of two equations word problems
- Points in three dimensions
- Planes
- Solving systems of three linear equations by elimination
- Solving systems of three linear equations by substitution

**Polynomial Functions**

- Naming polynomials
- Adding / subtracting / multiplying polynomials
- The Binomial Theorem
- Dividing polynomials
- Factoring by grouping
- Factoring sum/difference of cubes
- Factoring quadratic form
- Synthetic division and synthetic substitution
- The Remainder Theorem and The Factor Theorem
- Imaginary Root Theorem and Irrational Root Theorem
- Polynomials, factors, and roots
- Writing polynomial functions
- The Rational Root Theorem
- Descartes’ Rule of Signs
- The Fundamental Theorem of Algebra
- Solving polynomial equations, all methods
- End behavior of polynomial functions
- Sketching the general shape of polynomial functions
- Graphing polynomial functions, including minima/maxima
- Solving polynomial functions by graphing

**Trigonometry**

- Angles and angle measure
- Radians and degrees
- Coterminal angles
- Arc length and sector area
- Right triangle trig.
- Trig. functions of general angles
- The Law of Sines
- The Law of Cosines
- Heron’s Formula
- Graphing trig. functions
- Translations of trig. functions
- Angle sum and angle difference identities
- Half-angle and double-angle identities
- Trig. equations, neither factoring nor identities required